Problem: Simplify the following expression: $z = \dfrac{r + 6}{2r + 3} - \dfrac{-7r + 14}{2r + 3}$
Since the expressions have the same denominator we simply subtract the numerators: $z = \dfrac{r + 6 - (-7r + 14)}{2r + 3}$ Distribute the negative sign: $z = \dfrac{r + 6 + 7r - 14}{2r + 3}$ Combine like terms: $z = \dfrac{8r - 8}{2r + 3}$